64 research outputs found
New symmetries for the Gravitational S-matrix
In [15] we proposed a generalization of the BMS group G which is a semidirect
product of supertranslations and smooth diffeomorphisms of the conformal
sphere. Although an extension of BMS, G is a symmetry group of asymptotically
flat space times. By taking G as a candidate symmetry group of the quantum
gravity S-matrix, we argued that the Ward identities associated to the
generators of Diff(S^2) were equivalent to the Cachazo-Strominger subleading
soft graviton theorem. Our argument however was based on a proposed definition
of the Diff(S^2) charges which we could not derive from first principles as G
does not have a well defined action on the radiative phase space of gravity.
Here we fill this gap and provide a first principles derivation of the
Diff(S^2) charges. The result of this paper, in conjunction with the results of
[4, 15] prove that the leading and subleading soft theorems are equivalent to
the Ward identities associated to G.Comment: 19 page
Asymptotic symmetries of gravity and soft theorems for massive particles
The existing equivalence between (generalized) BMS Ward identities with
leading and subleading soft graviton theorems is extended to the case where the
scattering particles are massive scalars. By extending the action of
generalized BMS group off null infinity at late times, we show that there is a
natural action of such group not only on the radiative data at null infinity
but also on the scattering data of the massive scalar field. This leads to a
formulation of Ward identities associated to the generalized BMS group when the
scattering states are massive scalars or massless gravitons and we show that
these Ward identities are equivalent to the leading and subleading soft
graviton theorems.Comment: 30 page
Sub-subleading soft gravitons: New symmetries of quantum gravity?
Due to seminal works of Weinberg, Cachazo and Strominger we know that tree
level quantum gravity amplitudes satisfy three factorization constraints.
Building on previous works which relate two of these constraints to symmetries
of quantum gravity at null infinity, we present rather strong evidence that the
third constraint is also equivalent to a new set of symmetries of
(perturbative) quantum gravity. Our analysis implies that the symmetry group of
quantum gravity may be even richer than the BMS group (or infinite dimensional
extension thereof) previously considered.Comment: 5 page
Asymptotic symmetries of QED and Weinberg's soft photon theorem
Various equivalences between so-called soft theorems which constrain
scattering amplitudes and Ward identities related to asymptotic symmetries have
recently been established in gauge theories and gravity. So far these
equivalences have been restricted to the case of massless matter fields, the
reason being that the asymptotic symmetries are defined at null infinity. The
restriction is however unnatural from the perspective of soft theorems which
are insensitive to the masses of the external particles.
In this work we remove the aforementioned restriction in the context of
scalar QED. Inspired by the radiative phase space description of massless
fields at null infinity, we introduce a manifold description of time-like
infinity on which the asymptotic phase space for massive fields can be defined.
The "angle dependent" large gauge transformations are shown to have a well
defined action on this phase space, and the resulting Ward identities are found
to be equivalent to Weinberg's soft photon theorem.Comment: 19 pages, no figure
Loop Corrected Soft Photon Theorem as a Ward Identity
Recently Sahoo and Sen obtained a series of remarkable results concerning
sub-leading soft photon and graviton theorems in four dimensions. Even though
the S- matrix is infrared divergent, they have shown that the sub-leading soft
theorems are well defined and exact statements in QED and perturbative Quantum
Gravity. However unlike the well studied Cachazo-Strominger soft theorems in
tree-level amplitudes, the new sub-leading soft expansion is at the order ln
{\omega} (where {\omega} is the soft frequency) and the corresponding soft
factors structurally show completely different properties then their tree-level
counterparts. Whence it is natural to ask if these theorems are associated to
asymptotic symmetries of the S-matrix. We consider this question in the context
of sub-leading soft photon theorem in scalar QED and show that there are indeed
an infinity of conservation laws whose Ward identities are equivalent to the
loop-corrected soft photon theorem. This shows that in the case of four
dimensional QED, the leading and sub-leading soft photon theorems are
equivalent to Ward identities of (asymptotic) charges.Comment: 33 pages, no figure
Asymptotic charges at spatial infinity
Large gauge symmetries in Minkowski spacetime are often studied in two
distinct regimes: either at asymptotic (past or future) times or at spatial
infinity. By working in harmonic gauge, we provide a unified description of
large gauge symmetries (and their associated charges) that applies to both
regimes. At spatial infinity the charges are conserved and interpolate between
those defined at the asymptotic past and future. This explains the equality of
asymptotic past and future charges, as recently proposed in connection with
Weinberg's soft photon theorem.Comment: 23 page
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